Jacob's approximation in flow through porous media
Journal Article
·
· Water Resour. Res.; (United States)
The equation of flow of slightly compressible fluids through nondeformable, or consolidating, porous media is a nonlinear parabolic partial differential equation of the second order. Previously, the equation has been approximately linearized by neglecting its nonlinear term. This method of linearization, hereafter called Jacob's method, was first introduced by C.E. Jacob for flow of ground water in confined aquifers. In this work the method of functional transformation was used to find a transformation which exactly linearized the equation. A problem of constant drawdown well in extensive homogeneous and isotropic consolidating, or nondeformable, porous media was solved. Solution of the approximate linearized differential equation for the problem was compared with the exact one, and the error due to the neglect of the nonlinear term was analyzed. It is shown that the error resulting from Jacob's approximate method of linearization for flow of water through confined aquifers is negligible. However, in the case of the transport of other compressible fluids through nondeformable formations the error is significant. 10 references.
- OSTI ID:
- 6252458
- Journal Information:
- Water Resour. Res.; (United States), Journal Name: Water Resour. Res.; (United States) Vol. 16:2; ISSN WRERA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
58 GEOSCIENCES
580100 -- Geology & Hydrology-- (-1989)
AQUIFERS
DIFFERENTIAL EQUATIONS
DRAWDOWN
ENERGY SOURCES
ENHANCED RECOVERY
EQUATIONS
FLOW MODELS
FLUID FLOW
FLUID INJECTION
FLUIDS
FOSSIL FUELS
FUELS
GROUND WATER
HYDROGEN COMPOUNDS
MATERIALS
MATHEMATICAL MODELS
OXYGEN COMPOUNDS
PARTIAL DIFFERENTIAL EQUATIONS
PETROLEUM
POROUS MATERIALS
RECOVERY
RESERVOIR FLUIDS
RESERVOIR PRESSURE
RESERVOIR ROCK
WATER
WATER TABLES
WATERFLOODING
WELL PRESSURE
020300* -- Petroleum-- Drilling & Production
58 GEOSCIENCES
580100 -- Geology & Hydrology-- (-1989)
AQUIFERS
DIFFERENTIAL EQUATIONS
DRAWDOWN
ENERGY SOURCES
ENHANCED RECOVERY
EQUATIONS
FLOW MODELS
FLUID FLOW
FLUID INJECTION
FLUIDS
FOSSIL FUELS
FUELS
GROUND WATER
HYDROGEN COMPOUNDS
MATERIALS
MATHEMATICAL MODELS
OXYGEN COMPOUNDS
PARTIAL DIFFERENTIAL EQUATIONS
PETROLEUM
POROUS MATERIALS
RECOVERY
RESERVOIR FLUIDS
RESERVOIR PRESSURE
RESERVOIR ROCK
WATER
WATER TABLES
WATERFLOODING
WELL PRESSURE